Till now, bicycles using internal speed-changing systems have become more and more popular on the market. Compared with an external speed-changing system, the internal speed-changing system has the characteristics of simple appearance, maintenance-free property and the like, and thus is very suitable for urban bicycles and shared bicycle systems. There is a huge market demand for the internal speed-changing system and it is a kind of high-tech and high value-added product. At present, there are two internal three-speed specifications on the market, and the two specifications of internal three-speed are of single-clutch structures. One is to push the clutch to change the speed through a push rod, and the other one is to pull the clutch to change the speed through a chain. The push rod or the chain for internal three-speed speed-changing is positioned on the right side of the forwarding direction of the bicycle, namely, on the right side of the clutch. For the internal three-speed of pushing the clutch to change the speed through the push rod, the advantage is light speed-changing hand feeling, but the speed-changing response is relatively slow. For the internal three-speed of pulling the clutch to change the speed through the chain, the advantage is that the internal three-speed responses fast in changing, but the speed-changing hand feeling is heavy. However, there is no transmission combining the advantages of the above-mentioned two types of internal three-speed on the market.